Frank Hellmann

Iva Bačić, Jakob Niehues, Philipp C. Böttcher et al.

Dynamic grid stability is traditionally ensured with synchronous generators. Modern grids rely substantially more on inverter-based resources, which require grid-forming control to guarantee adequate system-wide synchronization and stability. Small-signal stability has granted various centralized and decentralized stability certificates - but these have primarily been limited to sufficient criteria only. In this work, we construct a necessary and sufficient small-signal stability criterion for lossless inverter-based power grids with arbitrary topology. We show that asymptotic stability is equivalent to the positive definiteness of a single matrix that combines network topology, operating point, and effective droop gains. We derive graph-theoretic stability criteria based on an augmented cone graph and show that the contribution of graph cycles is typically small, as illustrated for three IEEE test cases. The resulting framework yields decentralized stability criteria, quantifies the conservatism introduced by decentralization, and may support the development of future grid codes.

Christian Nauck, Junyou Zhu, Michael Lindner et al.

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

Nubius Brandner, Frank Hellmann, Hans Würfel et al.

Large-scale power outages are typically caused by cascading failures. These unfold dynamically through complex interactions between network dynamics and individual component failures. In contrast, the study of cascading failures in physics has focused on analyzing line overloads in the quasi-static regime. We introduce a new model that integrates the dynamics of node and line failures with a paradigmatic oscillator model for power grid synchronization. This enables us to investigate the collective cascading behavior of coupled failures for the first time. We study the impact of nodal robustness, the ability of nodes to tolerate transient disturbances, and inertia, the ability of nodes to resist frequency deviations, on cascade sizes. We discover two novel mechanisms driving system fragility: i) While low inertia is widely considered a major challenge for power grids, we find that high inertia can amplify cascade sizes unless accompanied by appropriate adjustments of other dynamical properties. ii) Further, we find that an increase in the robustness of individual nodes can paradoxically lead to larger cascades. This latter phenomenon constitutes a novel type of Braess's paradox. Understanding such counterintuitive collective effects may become central for achieving resilient future power grids.